Question

The two angles of a quadrilateral are 70° and 110°. If out of the two remaining angles, one angle is 20°
more than the other, find the two angles.

please answer, I will mark you brainlist ​

Answer 1

★Given:-

• The two angles of a quadrilateral are 70° and 110°.
• Out of the two remaining angles, one angle is 20° more than the other.

★To find:-

• The two angles.

★Solution:-

We know,

✦A quadrilateral is a plane figure having 4 sides.

✦Sum of all interior angles add up to 360°.

Let one of the remaining angle is 'x'.

Then according to question,

• Other angle = x + 20

We have,

• Given two angles are  70° and 110°.
• Remaining angles are x & x+20.

Applying the angle sum property of quadrilaterals,

➔70+110 + x + x+20 = 360

➔200 + 2x = 360

➔2x = 360-200

➔2x = 160

➔x = 160/2

➔x = 80°

Now, we have:

• Other angle = x + 20

Substituting value of x,

➔x + 20 = 80 + 20  

          = 100°

Therefore,

The two angles are 80° & 100°

______________

✯Verification✯

We know,

Sum of all angles of a quadrilateral is 360°.

Putting values,

➔70+110+100+80

➔360.

Hence verified.

______________

Answer 2

$\huge\pink{\mid{\fbox{\tt{your\:QUESTION}}\mid}}$

The two angles of a quadrilateral are 70° and 110°. If out of the two remaining angles, one angle is 20° more than the other, find the two angles.

To find:

Two angles.

$\huge\red{\mid{\underline{\overline{\textbf{Solution\:࿐}}}\mid}}$

As We know,

☆A quadrilateral is a plane figure having 4 sides.

☆Sum of all interior angles add up to 360°.

so,

Let one of the remaining angle is 'x'.

Then according to question,

Other angle = x + 20

We have,

Given two angles are  70° and 110°.

Remaining angles are x & x+20.

Applying angle sum property of quadrilaterals,

➪70+110 + x + x+20 = 360

➪200 + 2x = 360

➪2x = 360-200

➪2x = 160

$x = \frac{160}{2}$

➪x = 80°

Now, we have:

Other angle = x + 20

Substituting value of x,

➪x + 20 = 80 + 20  

          = 100°

.'.

The two angles are 80° & 100°

☆Verification☆

As we know,

Sum of all angles of a quadrilateral is 360°.

~~Putting values,

➪70+110+100+80

➪360.

verified!

$\sf\red{hope\:it\:helps\:you}$